Finite Group Databasebeta

← #14909584

Subgroups — #14909584

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078199C211yesmaximal, characteristic
2C2×#10622801C211yesmaximal, characteristic, complemented
3#13070822C212yesmaximal, complemented
4#13070816C211yesmaximal, characteristic, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070732C212yesmaximal, complemented
7#13070721C212yesmaximal, complemented
8#13070555C212yesmaximal, complemented
9#13070533C211yesmaximal, characteristic, complemented
10#13070225C211yesmaximal, characteristic, complemented
11C11×#2188C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#66999—21no—
14C2×#66972C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16#10623158—21no—
17C2×C11×Q32C2212yescomplemented
18C11×#467C2211yescharacteristic
19C2×#66899—21no—
20#10622801—21no—
21#10622801—21no—
22#10622801C2211yescharacteristic
23#10622801C2212yes—
24#10622801C2212yes—
25C2×#66892C2212yescomplemented
26#10622728C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28#10622661—21no—
29C2×#66862C2212yes—
30#10622496C2211yescharacteristic
31#10622493C2211yescharacteristic
32#10622420—21no—
33#10622417—21no—
34C11×#358C2212yescomplemented
35C11×C22⋊C16C2211yescharacteristic
36#10622202C2212yescomplemented
37#10622202C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic
39#10622147C2212yescomplemented
40(C2×D11)⋊C16C2212yes—
41#10622143C2212yescomplemented
42#10622127C2212yescomplemented
43C22×Q8×C11—21no—
44C2×#4343—21no—
45C22×C4×D11D411yescharacteristic
46C2×C11×Q16—21no—
47C2×C11×Q16—42no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×Q16C2312yes—
50C22×C8×C11C2311yescharacteristic
51C11×C22⋊Q8—21no—
52#66999—22no—
53#66999—22no—
54#66999—21no—
55#66999—41no—
56#66999—41no—
57C2×#4325—21no—
58#66983—21no—
59C2×(C2×D11)⋊C4—41no—
60C2×C4⋊Dic11—21no—
61C2×Dic11⋊C4—41no—
62C22×C11⋊C8D411yescharacteristic
63#66972—42no—
64C2×D88C2311yescharacteristic
65C2×C8×D11—42no—
66C2×C8×D11D411yescharacteristic
67C2×C8×D11D411yescharacteristic
68C2×C8×D11C2311yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66948—21no—
71#66947—41no—
72#66946—41no—
73#66945—21no—
74#66935—41no—
75(C22⋊D11)⋊C4—41no—
76C11×Q32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#103—21no—
80#66899—22no—
81#66899—22no—
82#66899—21no—
83#66892—42no—
84#66885—21no—
85#66882—21no—
86#66882C2311yescharacteristic
87#66882C2312yes—
88C2×C11⋊C16C2312yes—
89#66873—21no—
90#66872—21no—
91#66862—42no—
92#33762—111nomaximal, Sylow
93C23×D11D811yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—41no—
102C22×Dic11—41no—
103C22×Dic11D811yescharacteristic
104#4343—42no—
105#4343—42no—
106C2×D44—21no—
107C2×D44—41no—
108C2×D44—41no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11D811yescharacteristic
113C2×C4×D11D811yescharacteristic
114C2×C4×D11C2×D411yescharacteristic
115C2×C4×D11C2×D411yescharacteristic
116C11×Q16—22no—
117C11×Q16—22no—
118C11×Q16—22no—
119C11×Q16—42no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—21no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—41no—
126#4325—42no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—41no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—41no—
136Dic11⋊C4—41no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139C4×Dic11—41no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8C2×D411yescharacteristic
142C2×C11⋊C8C2×D411yescharacteristic
143D88—22no—
144C8×D11—22no—
145C8×D11—22no—
146C8×D11—41no—
147C8×D11—41no—
148C11×C16—22no—
149C11⋊C16—22no—
150#3050—111no—
151C2×#467—111no—
152#2237—112no—
153#2236—111no—
154#2233—111no—
155#2220—112no—
156#2219—112no—
157#2189—112no—
158#2188D1111yescharacteristic, complemented
159#2185—111no—
160#2112—111no—
161C23×C11C2×D811yescharacteristic
162C22×D11—22no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11C2×D811yescharacteristic
167C22×D11C2×D811yescharacteristic
168Q8×C11—41no—
169Q8×C11—42no—
170Q8×C11—41no—
171Q8×C11—42no—
172Q8×C11—82no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—82no—
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—82no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—82no—
186C2×Dic11C2×D811yescharacteristic
187C2×Dic11C2×D811yescharacteristic
188D44—41no—
189D44—41no—
190D44—82no—
191D44—82no—
192C4×D11—21no—
193C4×D11—21no—
194C4×D11—21no—
195C4×D11—21no—
196C4×D11—41no—
197C4×D11—41no—
198C4×D11—82no—
199C8×C11—21no—
200C8×C11H(5,𝔽2)12yes—
201C11⋊C8—21no—
202C11⋊C8—21no—
203C2×#135—111no—
204C22×Q16C2×D1111yescharacteristic
205C23×C8—111no—
206#525—221no—
207C2×C22⋊Q8—221no—
208C2×Q32C2×D1112yescomplemented
209C2×SD32—112no—
210C2×M32—112no—
211#467—112no—
212#467—111no—
213#467—112no—
214#467—221no—
215#467—221no—
216#467C2×D1111yescharacteristic
217#466—111no—
218#466—111no—
219#465—221no—
220#465—221no—
221#427—111no—
222C2×#107—111no—
223#416—221no—
224C2×#103—221no—
225#367—112no—
226#366—112no—
227#358—112no—
228#358—112no—
229#358C2×D1112yescomplemented
230#357—112no—
231C22⋊C16—111no—
232C22⋊C16—112no—
233C22⋊C16C2×D1111yescharacteristic
234C22×C11—21no—
235C22×C11—21no—
236C22×C11#51012yes—
237C22×C11C22×D811yescharacteristic
238C2×D11—21no—
239C2×D11—21no—
240C2×D11—21no—
241C2×D11—21no—
242C2×D11—21no—
243C2×D11—21no—
244C2×D11—44no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—82no—
251C4×C11—81no—
252C4×C11#53411yescharacteristic
253C4×C11#57511yescharacteristic
254Dic11—21no—
255Dic11—21no—
256Dic11—81no—
257Dic11—82no—
258C2×#41—221no—
259C22×Q8—21no—
260C23×C4—111no—
261#135—442no—
262C2×Q16—21no—
263C2×Q16—42no—
264C2×Q16C22×D1112yes—
265C2×Q16C22×D1111yescharacteristic
266C2×SD16—221no—
267C2×D8—111no—
268C22×C8—111no—
269C22×C8—111no—
270C22×C8—111no—
271C22×C8—111no—
272C22×C8—111no—
273C22×C8—442no—
274C22×C8C22×D1111yescharacteristic
275#123—441no—
276C22⋊Q8—21no—
277C22⋊Q8—222no—
278C22⋊Q8—222no—
279C22⋊Q8—221no—
280C22⋊Q8—441no—
281C22⋊Q8—441no—
282#121—221no—
283#121—221no—
284#120—441no—
285C4×D4—441no—
286C4×D4—441no—
287#117—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—441no—
290C2×C22⋊C4—441no—
291Q32—42no—
292SD32—442no—
293M32—442no—
294C2×C16—112no—
295C2×C16C22×D1112yes—
296#107—112no—
297#107—111no—
298#107—221no—
299#107C22×D1111yescharacteristic
300#106—221no—
301#103—21no—
302#103—222no—
303#103—222no—
304#103—221no—
305#102—221no—
306#102—221no—
307C2×C11—22no—
308C2×C11#318611yescharacteristic
309C2×C11C2×#51011yescharacteristic
310C2×C11#341411yescharacteristic
311D11—41no—
312D11—41no—
313D11—161no—
314C24—111no—
315#41—442no—
316#41—442no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—42no—
320C2×Q8—42no—
321C2×Q8—41no—
322C2×D4—221no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C22×C4—41no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4—441no—
336C22×C4D4×D1111yescharacteristic
337Q16—22no—
338Q16—22no—
339Q16—22no—
340Q16—42no—
341SD16—442no—
342D8—222no—
343C2×C8—22no—
344C2×C8—111no—
345C2×C8—111no—
346C2×C8—222no—
347C2×C8—222no—
348C2×C8—441no—
349C2×C8—441no—
350C2×C8—441no—
351C2×C8D4×D1111yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—41no—
355C4⋊C4—221no—
356C4⋊C4—222no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—41no—
362C22⋊C4—441no—
363C22⋊C4—442no—
364C22⋊C4—442no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C42—441no—
369C16—22no—
370C16—222no—
371C11#3376211yescharacteristic, complemented, Sylow
372C23—111no—
373C23—111no—
374C23—222no—
375C23—441no—
376C23—441no—
377C23—441no—
378C23D8×D1111yescharacteristic
379Q8—42no—
380Q8—41no—
381Q8—41no—
382Q8—42no—
383Q8—82no—
384D4—441no—
385D4—441no—
386D4—882no—
387D4—882no—
388D4—882no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—111no—
396C2×C4—111no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—442no—
406C2×C4—882no—
407C2×C4—882no—
408C2×C4D8×D1111yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C8—21no—
411C8—221no—
412C8—221no—
413C8#6703712yes—
414C22—21no—
415C22—21no—
416C22—221no—
417C22—221no—
418C22—221no—
419C22—221no—
420C22—221no—
421C22—221no—
422C22—444no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22#1062253112yes—
427C22C2×D8×D1111yescharacteristic
428C4—21no—
429C4—82no—
430C4—81no—
431C4—81no—
432C4—221no—
433C4—221no—
434C4—881no—
435C4—882no—
436C4#1062312011yescharacteristic
437C4#1062330411yescharacteristic
438C2—22no—
439C2—441no—
440C2—441no—
441C2—1761no—
442C2#1307936511yescharacteristic
443C2C2×#1062253111yescharacteristic
444C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radical#13078199C2
hypercenter#2188D11
hypocenterC11#33762
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622801C2semidirect
3. #13070822C2semidirect
4. #13070816C2semidirect
5. #13070802C2semidirect
6. #13070732C2semidirect
7. #13070721C2semidirect
8. #13070555C2semidirect
9. #13070533C2semidirect
10. #13070225C2semidirect
11. C11×#2188C2semidirect
17. C2×C11×Q32C22semidirect
25. C2×#66892C22semidirect
34. C11×#358C22semidirect
36. #10622202C22semidirect
37. #10622202C22semidirect
39. #10622147C22semidirect
41. #10622143C22semidirect
42. #10622127C22semidirect
158. #2188D11semidirect
208. C2×Q32C2×D11semidirect
229. #358C2×D11semidirect
371. C11#33762semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130781992
C2×#106228012
#130708222
#130708162
#130708022
#130707322
#130707212
#130705552
#130705332
#130702252
C11×#21882
#3376211